IPMAT Indore (MCQ) PYQs

If $f\left(x^{2}+f(y)\right)=x f(x)+y$ for all non-negative integers $x$ and $y$, then the value of $[f(0)]^{2}+f(0)$ equals _________.

Let $A=\{1,2,3\}$ and $B=\{a, b\}$. Assuming all relations from set $A$ to set $B$ are equally likely, what is the probability that a relation from $A$ to $B$ is also a function?

Given $f(x) = x^2 + \log_3 x$ and $g(y) = 2y + f(y)$, then the value of $g(3)$ equals